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Course11110376460 lectures

Calculus - II

Prof. M. Guru Prem Prasad Prof. Arup Chattopadhyay · IIT Guwahati

Start with lecture 1 At NPTEL

Lectures

Week 1

  1. Lec 1: Coordinates Systems 2-D and 3-D Video
  2. Lec 2: Vector Algebra R^n Video
  3. Lec 3: Euclidean space R^n and some of its properties Video
  4. Lec 4: Sequences in R^n Video

Week 2

  1. Lec 5: Functions of Several Variables and Concept of Limit Video
  2. Lec 6: Properties of Limit, Iterated Limit and Double limit Video
  3. Lec 7: Concept of Continuity and Some of Its Properties Video
  4. Lec 8: Properties of Continuous Functions Video
  5. Lec 9: Concept of Differentiability for Vector-valued Functions Video
  6. Lec 10: Properties of Differentiable Functions, Chain Rule Video
  7. Lec 11: Applications of Differentiability Video

Week 3

  1. Lec 12: Concept of Partial Derivates, Examples and Properties Video
  2. Lec 13: Higher order Partial Derivatives and notion of Directional Derivatives Video
  3. Lec 14: Concept of Total Derivative and related properties Video
  4. Lec 15: Gradient Vector and Necessary condition for Differentiability Video
  5. Lec 16: Sufficient condition for Differentiability and Chain rule Video
  6. Lec 17: Applications: Tangent Plane and Normal Line for a Surface Video

Week 4

  1. Lec 18: Mixed Partial Derivatives and Examples Video
  2. Lec 19: Mixed Derivative Theorem and Examples Video
  3. Lec 20: Concept of Mean Value Theorem Video
  4. Lec 21: Notion of Hessian Video
  5. Lec 22: Taylor’s theorem and Linear approximation Video

Week 5

  1. Lec 23: Maxima, Minima and Saddle point Video
  2. Lec 24: Necessary condition for extremum and quadratic forms Video
  3. Lec 25: Hessian matrix, Method to find the extremum values of f Video
  4. Lec 26: Global extrema, Constrained extrema Video
  5. Lec 27: The method of Lagrange multiplies, Exact differentials. Video

Week 6

  1. Lec 28: Definition of Double integrals in terms of Upper and Lower sums Video
  2. Lec 29: Definition of Double integrals in terms of Riemaan Sum and Properties Video
  3. Lec 30: Iterated integral and Fubini’s theorem Video
  4. Lec 31: Double integral on simple regions and Fubini’s theorem Video
  5. Lec 32: Change of Variables in a Double Integral and Applications Video

Week 7

  1. Lec 33: Definition of Triple integrals as Riemann Integral and Examples Video
  2. Lec 34: Triple integral on simple regions and Fubini’s theorem Video
  3. Lec 35: More on Triple integral on simple regions and Fubini’s theorem Video
  4. Lec 36: Change of Variables in Triple Integral and Examples Video

Week 8

  1. Lec 37: Definition of Vector Fields and visualization of them by arrows Video
  2. Lec 38: Integral curves of Vector Fields, conservative and non-conservative vector fields, Gradient Video
  3. Lec 39: Necessary and sufficient conditions for a conservative/gradient vector field. Video
  4. Lec 40: Concept of Divergence and Curl Video
  5. Lec 41: Curl, rotational vector field, Divergence of curl, Laplace operator Video

Week 9

  1. Lec 42: Recall of Curves, Smooth Curves, Piecewise Smooth Curves Video
  2. Lec 43: Definition of Scalar Line Integral, Some examples and properties Video
  3. Lec 44: Orientation of smooth curve and definition of Vector Line Integral Video
  4. Lec 45: Definition of Vector Line Integral, Examples , Properties and Applications Video

Week 10

  1. Lec 46: Definition of surfaces, smooth surfaces, and parametrization of surfaces Video
  2. Lec 47: Definition of scalar surface integral and some examples Video
  3. Lec 48: Oriented surfaces and the definition of vector surface integral Video
  4. Lec 49: Vector surface integral and some examples Video

Week 11

  1. Lec 50: Recall the definition of curves, orientation of curves, Jordan curve theorem. Video
  2. Lec 51: Statement, and proof of Green's theorem ona simply connected region Video
  3. Lec 52: Application of Green's theorem and Green's theorem for multiply connected regions. Video
  4. Lec 53: Application of Green's theorem for multiply connected regions and Examples. Video

Week 12

  1. Lec 54: Recall the definition of surfaces, smooth surfaces, and orientation of surfaces Video
  2. Lec 55: Oriented surfaces, Stokes theorem on smooth surfaces with examples Video
  3. Lec 56: Stokes theorem on smooth surfaces with finitely many holes, Gauss Divergence theorem and examples Video
  4. Lec 57: Gauss Divergence theorem, Application of Divergence theorem and examples Video

Live Session

  1. Live Session 21-08-2025 Video
  2. Live Session 22-09-2025 Video
  3. Live Session 10-10-2025 Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Guwahati
Department
Mathematics
Teacher
Prof. M. Guru Prem Prasad Prof. Arup Chattopadhyay
Level
Undergraduate
Language
English
Subjects
Mathematics
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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